Bijection

This page is a dire page and is in desperate need of an update.

The message is:

This must have been one of the first pages, from Feb 2015!

A bijection is a 1:1 map. A map which is both injective and surjective.

It has the useful property that for

$$f:X\rightarrow Y$$ that $$f^{-1}(y)$$ is always defined, and is at most one element.

Thus

$$f^{-1}$$ behaves as a normal function (rather than the always-valid but less useful $$f^{-1}:Y\rightarrow\mathcal{P}(X)$$ where $$\mathcal{P}(X)$$ denotes the power set of $$X$$ )

Statements to add (to new version of the page, 'cos current version is dire)

• Every bijection yields an inverse function